Envelope binding energies E_bind of massive giants (i.e., the post-MS part of the evolution) as a function of their radius for six different metallicities (selected models from Klencki et al. 2020). See Fig. C.1 for a figure including all the masses in the grid and Fig. C.3 for a figure showing all the corresponding λ_CE values. E_bind combines the gravitational potential energy as well as the internal energy (including the recombination terms); see Eq. (3). Only post-MS evolution is shown. Colors indicate what fraction of the envelope mass is in the outer convective zone (i.e., M_env; conv/M_env). Diamonds (same coloring) and white crosses mark the onset and end of core-helium burning, respectively. Part of the evolution when the radius is increasing beyond the previously largest radius that has been reached, i.e., the part relevant for RLOF and mass transfer, is shaded in black. Development of a deep outer convective envelope layer can lead to a very significant decrease in the binding energy, unless the giant is a HG star (i.e., before the core-helium ignition); see Sect. 3.4 for details.